%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:06:42 PM UTC 2026
% Result : Theorem 1.78s 1.27s
% Output : CNFRefutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 21 unt; 0 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 38 ~; 34 |; 2 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 6 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 0 sgn 64 !; 1 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( modus_ponens
<=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',modus_ponens) ).
fof(f4,axiom,
( implies_1
<=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_1) ).
fof(f5,axiom,
( implies_2
<=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',implies_2) ).
fof(f12,axiom,
( or_3
<=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',or_3) ).
fof(f22,axiom,
( r1
<=> ! [X0] : is_a_theorem(implies(or(X0,X0),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',r1) ).
fof(f35,axiom,
modus_ponens,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_modus_ponens) ).
fof(f37,axiom,
implies_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_1) ).
fof(f38,axiom,
implies_2,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_implies_2) ).
fof(f45,axiom,
or_3,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_or_3) ).
fof(f53,conjecture,
r1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',principia_r1) ).
fof(f54,negated_conjecture,
~ r1,
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f55,plain,
~ r1,
inference(flattening,[],[f54]) ).
fof(f56,plain,
( ! [X0] : is_a_theorem(implies(or(X0,X0),X0))
=> r1 ),
inference(unused_predicate_definition_removal,[],[f22]) ).
fof(f60,plain,
( or_3
=> ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f67,plain,
( implies_2
=> ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f68,plain,
( implies_1
=> ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f71,plain,
( modus_ponens
=> ! [X0,X1] :
( ( is_a_theorem(implies(X0,X1))
& is_a_theorem(X0) )
=> is_a_theorem(X1) ) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f72,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(ennf_transformation,[],[f71]) ).
fof(f73,plain,
( ~ modus_ponens
| ! [X0,X1] :
( ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ) ),
inference(flattening,[],[f72]) ).
fof(f76,plain,
( ~ implies_1
| ! [X0,X1] : is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(ennf_transformation,[],[f68]) ).
fof(f77,plain,
( ~ implies_2
| ! [X0,X1] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(ennf_transformation,[],[f67]) ).
fof(f84,plain,
( ~ or_3
| ! [X0,X1,X2] : is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(ennf_transformation,[],[f60]) ).
fof(f88,plain,
( ? [X0] : ~ is_a_theorem(implies(or(X0,X0),X0))
| r1 ),
inference(ennf_transformation,[],[f56]) ).
fof(f94,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| r1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f88]) ).
fof(f95,plain,
! [X0,X1] :
( ~ modus_ponens
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0)
| is_a_theorem(X1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f98,plain,
! [X0,X1] :
( ~ implies_1
| is_a_theorem(implies(X0,implies(X1,X0))) ),
inference(cnf_transformation,[],[f76]) ).
fof(f99,plain,
! [X0,X1] :
( ~ implies_2
| is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))) ),
inference(cnf_transformation,[],[f77]) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ or_3
| is_a_theorem(implies(implies(X0,X2),implies(implies(X1,X2),implies(or(X0,X1),X2)))) ),
inference(cnf_transformation,[],[f84]) ).
fof(f110,plain,
( ~ is_a_theorem(implies(or(sK0,sK0),sK0))
| r1 ),
inference(cnf_transformation,[],[f94]) ).
fof(f119,plain,
modus_ponens,
inference(cnf_transformation,[],[f35]) ).
fof(f121,plain,
implies_1,
inference(cnf_transformation,[],[f37]) ).
fof(f122,plain,
implies_2,
inference(cnf_transformation,[],[f38]) ).
fof(f129,plain,
or_3,
inference(cnf_transformation,[],[f45]) ).
fof(f137,plain,
~ r1,
inference(cnf_transformation,[],[f55]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ modus_ponens
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,implies(X1,X0)))
| ~ implies_1 ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1)))
| ~ implies_2 ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1))))
| ~ or_3 ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_64,plain,
( r1
| ~ is_a_theorem(implies(or(sK0,sK0),sK0)) ),
inference(cnf_transformation,[],[f110]) ).
tcf(c_73,plain,
modus_ponens,
inference(cnf_transformation,[],[f119]) ).
tcf(c_75,plain,
implies_1,
inference(cnf_transformation,[],[f121]) ).
tcf(c_76,plain,
implies_2,
inference(cnf_transformation,[],[f122]) ).
tcf(c_83,plain,
or_3,
inference(cnf_transformation,[],[f129]) ).
tcf(c_91,negated_conjecture,
~ r1,
inference(cnf_transformation,[],[f137]) ).
tcf(c_96,plain,
( is_a_theorem(implies(sK0,implies(sK0,sK0)))
| ~ implies_1 ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_143,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,implies(X0,X1)),implies(X0,X1))),
inference(global_subsumption_just,[status(thm)],[c_53,c_76,c_53]) ).
tcf(c_149,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_49,c_73,c_49]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(X1)
| ~ is_a_theorem(X0)
| ~ is_a_theorem(implies(X0,X1)) ),
inference(renaming,[status(thm)],[c_149]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] : is_a_theorem(implies(implies(X0,X1),implies(implies(X2,X1),implies(or(X0,X2),X1)))),
inference(global_subsumption_just,[status(thm)],[c_60,c_83,c_60]) ).
tcf(c_715,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(X0,X1))
| ~ is_a_theorem(implies(X0,implies(X0,X1))) ),
inference(superposition,[status(thm)],[c_143,c_150]) ).
tcf(c_778,plain,
( is_a_theorem(implies(sK0,sK0))
| ~ is_a_theorem(implies(sK0,implies(sK0,sK0))) ),
inference(instantiation,[status(thm)],[c_715]) ).
tcf(c_2455,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(implies(X0,X1),implies(or(X0,X0),X1))),
inference(superposition,[status(thm)],[c_166,c_715]) ).
tcf(c_3311,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(or(X0,X0),X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_2455,c_150]) ).
tcf(c_3318,plain,
( is_a_theorem(implies(or(sK0,sK0),sK0))
| ~ is_a_theorem(implies(sK0,sK0)) ),
inference(instantiation,[status(thm)],[c_3311]) ).
tcf(c_3319,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3318,c_778,c_96,c_64,c_91,c_75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL454+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 23:29:38 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.40
% 0.13/0.40 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 1.78/1.27 % SZS status Started for theBenchmark.p
% 1.78/1.27 % SZS status Theorem for theBenchmark.p
% 1.78/1.27
% 1.78/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.78/1.27
% 1.78/1.27 % ------ iProver source info
% 1.78/1.27
% 1.78/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.78/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.78/1.27 % git: non_committed_changes: false
% 1.78/1.27
% 1.78/1.27 % ------ Parsing...
% 1.78/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.78/1.27
% 1.78/1.27 % ------ Preprocessing... sup_sim: 3 sf_s rm: 22 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.78/1.27
% 1.78/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.78/1.27
% 1.78/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.78/1.27 % ------ Proving...
% 1.78/1.27 % ------ Problem Properties
% 1.78/1.27
% 1.78/1.27 %
% 1.78/1.27 % clauses 21
% 1.78/1.27 % conjectures 0
% 1.78/1.27 % EPR 0
% 1.78/1.27 % Horn 21
% 1.78/1.27 % unary 19
% 1.78/1.27 % binary 1
% 1.78/1.27 % lits 24
% 1.78/1.27 % lits eq 6
% 1.78/1.27 % fd_pure 0
% 1.78/1.27 % fd_pseudo 0
% 1.78/1.27 % fd_cond 0
% 1.78/1.27 % fd_pseudo_cond 1
% 1.78/1.27 % AC symbols 0
% 1.78/1.27
% 1.78/1.27 % ------ Schedule dynamic 5 is on
% 1.78/1.27
% 1.78/1.27 % ------ no conjectures: strip conj schedule
% 1.78/1.27
% 1.78/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 1.78/1.27
% 1.78/1.27
% 1.78/1.27 % ------
% 1.78/1.27 % Current options:
% 1.78/1.27 % ------
% 1.78/1.27
% 1.78/1.27
% 1.78/1.27 %
% 1.78/1.27
% 1.78/1.27 % ------ Proving...
% 1.78/1.27 %
% 1.78/1.27
% 1.78/1.27 % SZS status Theorem for theBenchmark.p
% 1.78/1.27
% 1.78/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.78/1.28
% 1.78/1.28
%------------------------------------------------------------------------------